In this paper, we give the existence and uniqueness theorems for non-lightlike framed surfaces and define a special non-lightlike ruled surface in Minkowski 3-space. It may have singularities. We give the conditions for identifying cross-caps and surfaces as developable and maximal. Besides, we demonstrate that if the spacelike ruled surface is developable, then the $z$-parameter curve is an asymptotic curve if and only if the ruled surface is maximal.

In this paper, we define non-lightlike framed rectifying curves. They may have singularities. We give equivalent definitions and a construction method for non-lightlike framed rectifying curves. Moreover, we also study the relationship between the non-lightlike framed rectifying curves and the non-lightlike framed helices, as well as the properties of the centrode of non-lightlike framed rectifying curves.

In the present paper, we defined the circular evolutes and involutes for a given spacelike framed curve with respect to Bishop directions in Minkowski 3-space. Then, we studied the essential duality relations among parallel curves, normal surfaces, and circular evolutes and involutes. Furthermore, we also studied the duality relations of their singularities. Based on these studies, we found that it is crucially important to consider the duality relations among different geometric objects for the research of submanifolds with singularities.